The ratio of prices of Cello and Rotomac pens in 2000 were in the ratio of 3: 5. In 2005 the price of Cello pen tebles itself and the price of Rotomac pen is increased by ₹ 100, then the new ratio of prices of the same pens becomes 4 : 5. What was the original price of the Rotomac pen in 2000?

Options

A. ₹ 60
B. ₹ 80
C. ₹ 100
D. ₹ 120

Answer

To solve the problem, we will follow these steps:

1. **Define the Variables**: Let the price of Cello pen in 2000 be \(3x\) and the price of Rotomac pen in 2000 be \(5x\), where \(x\) is a common multiplier.

2. **Analyze the Changes in Prices**: In 2005, the price of the Cello pen doubles, so its new price becomes \(2 \times 3x = 6x\). The price of the Rotomac pen increases by ₹100, so its new price becomes \(5x + 100\).

3. **Set Up the New Ratio**: According to the problem, the new ratio of the prices of Cello and Rotomac pens in 2005 is \(4:5\). Therefore, we can set up the equation:
\[ \frac{6x}{5x + 100} = \frac{4}{5} \]

4. **Cross Multiply to Solve for \(x\)**: Cross multiplying gives us:
\[ 6x \cdot 5 = 4 \cdot (5x + 100) \]
Simplifying this, we have:
\[ 30x = 20x + 400 \]

5. **Isolate \(x\)**: Subtract \(20x\) from both sides:
\[ 30x - 20x = 400 \]
\[ 10x = 400 \]
Dividing both sides by 10 gives:
\[ x = 40 \]

6. **Calculate the Original Price of Rotomac Pen**: Since the original price of the Rotomac pen is \(5x\), we substitute \(x\) back into this expression:
\[ 5x = 5 \times 40 = 200 \]

Therefore, the original price of the Rotomac pen in 2000 was ₹200.